3d exceptional gauge theories and boundary confinement

TL;DR

This paper explores boundary confining dualities in 3d supersymmetric gauge theories with exceptional groups, linking boundary operator indices to special mathematical integrals and sums, and proposing new identities.

Contribution

It introduces novel boundary confining dualities for 3d $ ext{N}=2$ theories with exceptional gauge groups and derives new mathematical identities from these dualities.

Findings

Boundary indices match Askey-Wilson $q$-beta integrals and Macdonald sums.

New conjectural identities for $E_6$ and $E_7$ integrals and sums.

Boundary confinement of $ ext{N}=4$ vector multiplet theories.

Abstract

We find boundary confining dualities of 3d $\mathcal{N}=2$ supersymmetric gauge theories with exceptional gauge groups. The half-indices which enumerate the boundary BPS local operators in the presence of Neumann and Dirichlet boundary conditions for gauge fields are identified with the Askey-Wilson type $q$-beta integrals and Macdonald type sums respectively. New conjectural identities of $E_6$ and $E_7$ integrals and sums are derived from the boundary confining dualities. We also consider theories with a vector multiplet and adjoint chiral, which correspond to an $\mathcal{N}=4$ vector multiplet, with appropriate boundary conditions. We argue for the boundary confinement of the $\mathcal{N}=4$ vector multiplet and comment on such theories also with classical gauge groups.